Ground Band and a Generalized GP-equation for Spinor Bose-Einstein Condensates

TL;DR

This paper introduces a generalized Gross-Pitaevskii equation for spinor Bose-Einstein condensates that conserves both total spin and its Z-component, enabling more accurate modeling of ground state bands and level densities.

Contribution

It is the first to incorporate simultaneous conservation of total spin and its Z-component into the theoretical framework for spinor BECs, deriving a new generalized GP-equation.

Findings

Level splitting observed in ground bands of Na-23 and Rb-87 condensates.

Dense level distribution near the ground state for Na-23.

Dense levels at the top of the ground band for Rb-87.

Abstract

For the spinor Bose-Einstein condensates both the total spin $S$ and its Z-component $S_{Z}$ should be conserved. However, in existing theories, only the conservation of $S_{z}$ has been taken into account. To remedy, this paper is the first attempt to take the conservation of both $% S$ and $S_{Z}$ into account. For this purpose, a total spin-state with the good quantum numbers $S$ and $S_{Z}$ is introduced in the trial wave function, thereby a generalized Gross-Pitaevskii equation has been derived. With this new equation, the ground bands of the $^{23}$Na and $% ^{87}$Rb condensates have been studied, where the levels distinct in $S$ split. It was found that the level density is extremely dense in the bottom of the ground band of $^{23}$Na, i.e., in the vicinity of the ground state. On the contrary, for $^{87}$Rb, the levels are extremely dense in the top of the ground band,